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not breaking the individual components of each problem apart before performing the operation. 4 times 4 = 16, check, i times i equals i^2, which is? (student didn’t seem to know). one forth times 20, one over four times 20 over 1, then multiply. Student again didn’t look for components.

If I understand you correctly, Scott, then I disagree. All of these students did break a problem into components. For example, in the fraction problem the student took 1/4 and handled the 1 and the 4 separately.

I think I would actually say the opposite of Scott. The students don’t appear to have any real understanding of the concept being looked at, and therefore, has no understanding of what is acceptable in terms of breaking the problems apart. The different studetns attack these problems as if there are no relationships implied by the notations and numbers. They then “do some math” to the numbers, indifferent of those relationships.